1/3x=4/92x+3

Solution for 1/3x=4/92x+3 equation:

1/3x=4/92x+3

We move all terms to the left:

1/3x-(4/92x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 92x+3)!=0

x∈R


We get rid of parentheses

1/3x-4/92x-3=0

We calculate fractions


92x/276x^2+(-12x)/276x^2-3=0

We multiply all the terms by the denominator


92x+(-12x)-3*276x^2=0

Wy multiply elements

-828x^2+92x+(-12x)=0

We get rid of parentheses

-828x^2+92x-12x=0

We add all the numbers together, and all the variables

-828x^2+80x=0

a = -828; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-828)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-828}=\frac{-160}{-1656}
=20/207
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-828}=\frac{0}{-1656}
=0
$